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Technical Note—Complementary Programming

Author

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  • Toshihide Ibaraki

    (Kyoto University, Kyoto, Japan)

Abstract

A mathematical programming problem P : minimize z = d T x + e T u + f T v subject to Ax + Bu + Cv ≧ g , x , u , v ≧ 0, u T v = 0, is called a complementary programming ( CP ) problem. The condition u T v = 0 distinguishes CP problems from ordinary LP problems. A variety of nonlinear programming problems can be formulated in this form, including absolute-value programming problems, 0-1 mixed-integer-programming problems, quadratic-programming problems, and so forth. This paper proposes a branch-and-bound algorithm for CP problems and reports some computational results.

Suggested Citation

  • Toshihide Ibaraki, 1971. "Technical Note—Complementary Programming," Operations Research, INFORMS, vol. 19(6), pages 1523-1529, October.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:6:p:1523-1529
    DOI: 10.1287/opre.19.6.1523
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    Cited by:

    1. Francisco Jara-Moroni & John E. Mitchell & Jong-Shi Pang & Andreas Wächter, 2020. "An enhanced logical benders approach for linear programs with complementarity constraints," Journal of Global Optimization, Springer, vol. 77(4), pages 687-714, August.

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